Model and solve -3 1/2 + 2 3/4 on the vertical number line. Start at the first value and show the signed movement.
The filled point is the starting value. Draw the signed movement and endpoint; reveal answers only when checking work.
CCSS 7.NS.A.1b–c · horizontal & vertical number lines
Add and Subtract Rational Numbers on Number Lines
Model signed addition and subtraction as movement rather than memorized sign rules. Problems use exact integer, half, third, or quarter tick positions and rotate between horizontal and vertical number lines.
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Rational Numbers on Number Lines
Number-line addition & subtraction · Grade 7 standard · Seed 271701
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Model and solve -1 1/2 - 2 on the horizontal number line. Start at the first value and show the signed movement.
The filled point is the starting value. Draw the signed movement and endpoint; reveal answers only when checking work.
3.
Model and solve 1/4 - (-3) on the horizontal number line. Start at the first value and show the signed movement.
The filled point is the starting value. Draw the signed movement and endpoint; reveal answers only when checking work.
4.
Model and solve -2 1/4 + 3 on the vertical number line. Start at the first value and show the signed movement.
The filled point is the starting value. Draw the signed movement and endpoint; reveal answers only when checking work.
5.
Model and solve 1/2 - (-1) on the vertical number line. Start at the first value and show the signed movement.
The filled point is the starting value. Draw the signed movement and endpoint; reveal answers only when checking work.
6.
Model and solve -1/2 + (-1/4) on the vertical number line. Start at the first value and show the signed movement.
The filled point is the starting value. Draw the signed movement and endpoint; reveal answers only when checking work.
7.
Model and solve 3 1/2 - 1 on the horizontal number line. Start at the first value and show the signed movement.
The filled point is the starting value. Draw the signed movement and endpoint; reveal answers only when checking work.
8.
Model and solve 4 + (-1) on the horizontal number line. Start at the first value and show the signed movement.
The filled point is the starting value. Draw the signed movement and endpoint; reveal answers only when checking work.
9.
Model and solve -1 - (-1 1/2) on the horizontal number line. Start at the first value and show the signed movement.
The filled point is the starting value. Draw the signed movement and endpoint; reveal answers only when checking work.
10.
Model and solve 3 - 1 on the vertical number line. Start at the first value and show the signed movement.
The filled point is the starting value. Draw the signed movement and endpoint; reveal answers only when checking work.
Exact-construction rule: operations use normalized integer numerator/denominator pairs, number-line positions use exact ticks, repeating decimals come from remainder cycles, and money contexts use exact cents. No answer depends on binary floating-point rounding.
Signed addition and subtraction as movement
On a number line the sign rules become something you can see. Starting at the first number, adding moves in the direction of the sign of the second, and subtracting is rewritten as adding the opposite. The lines rotate between horizontal and vertical so students meet both a number line and a thermometer.
Movements on the line
- −1/2 + 1 1/4: start at −1/2 and move right 1 1/4 to land on 3/4.
- 1/4 − 3/4: rewrite as 1/4 + (−3/4), start at 1/4 and move left 3/4 to reach −1/2.
- On a vertical line, a change from −6 to +9 is a rise of 15 units.
- The distance between −2 1/2 and 1 1/2 is |1 1/2 − (−2 1/2)| = 4.
Confusions that appear on the line
- Moving in the wrong direction when subtracting a negative.
- Counting the starting point as the first step.
- Reporting distance as a negative number.
Connecting the picture to the rule
After three or four number-line problems, ask students to write the rule in their own words. The rules they discover from movement tend to stick better than rules stated before the practice, and the worksheet answer key includes the written expression that matches each drawn movement.
Common Core connection
- 7.NS.A.1 · Add and subtract rational numbers, using number lines and real-world contexts.
A practical match for the skill this worksheet practises, not a claim that one worksheet teaches or assesses the whole standard. Check the official math standards.
Note 1
For p + q, start at p and move in the direction indicated by the sign of q.
Note 2
For p - q, rewrite as p + (-q) before deciding the direction of movement.
Note 3
The distance between two rational numbers is the absolute value of their difference, regardless of left/right or up/down order.
Continue the 7.NS progression
Move to another Grade 7 rational-number skill
Quick answers
Do the lines include fractions?
Yes. Depending on level, the line can use whole-number, half, third, or quarter-unit ticks.
Why include vertical number lines?
The Grade 7 standard explicitly allows horizontal or vertical number-line diagrams, and vertical lines connect naturally to temperature and elevation contexts.